Your desktop software (perhaps Windows Explorer), has a database where programs can store an association between a file suffix and a program so that when you double-click on a file, the operating system will use that program. The installer software sets that up. That has nothing to do with the file format — that’s a configuration option of the desktop software.

On MacOS classic, each file had a “resource fork”, which was actually a second hidden file (they exist in version of Windows too, but are mostly unused). The resource fork file contained a code to indicate the file type, and the preferred program to open the file (usually set by the program that created it). The file name was completely irrelevant unless a program was written to filter by name.

Modern macOS would check to see if there was an extension and look up in text files what programs could open them and what the user has as a default. If the extension wasn’t recognized, then it would open the file and read part of it and use that to look up what format the file was (UNIX’ file method). There, the file extension was only important if given, because it was understood to be used by the user to o specify how to sort the files and which programs to use to open it.

Changing the file extension doesn’t change the data inside. If you rename a .jpg file .gif, it’s still a JPEG. If you have a desktop environment configured to open both with the same image editor (say, Photoshop), then double-clicking on the file tells Photoshop to open it. Photoshop then looks at the first few bytes of the file to see what’s inside. If it’s JPEG, it uses a routine to load JPEGs, even if the file has the .gif file extension.

Different formats store information in dramatically different ways, but many programs are capable of reading all sorts of data formats. Sometimes they pay attention to the file name, sometimes they don’t.